peak

peak

1. What Peak Value Is

Peak value ($V_m, I_m$) = maximum absolute value reached by alternating quantity in a cycle. Also called amplitude or crest value.

• For sine $v(t)=V_m sin ωt$, peak = $V_m$.
• Peak-to-peak $V_{p-p}=2V_m$ (for symmetric sine, square).
• Asymmetric waveforms may have different $+V_{peak}$ and $-V_{peak}$.

2. Why Peak Matters

• Insulation rating: must withstand $V_{peak}$ (not RMS) — 230V RMS mains peak 325V requires 600V insulation.
• Semiconductor PIV: diode must block $V_{peak}$.
• Crest factor = $V_m/V_{rms}$ indicates stress.

3. Worked Relation

Sine V_rms=230V ⇒ V_m=230·√2≈325V, V_p-p=650V ✓

Square wave V_m=5V ⇒ V_p-p=10V

If V_m=10V, average over full cycle 0, but peak remains 10V.

Need to select capacitor voltage rating > V_m plus safety.

4. Exam Points

• Define peak $V_m$ — 3 marks, very frequent.
• Relate $V_m$ to $V_{rms}$ for sine ($V_m=√2 V_{rms}$) — 5 marks, very frequent.
• Mention insulation/PIV uses peak — 3 marks.